Lemma 5.3 ([1]}, Lemma 6; see also [2]}, Lemma B.1)  
Let \(a \in C^{2}\left(\mathbb {T}^{3}\right)\) . For all \(1<p<+\infty \)  we have
\(\left\Vert |\nabla |^{-1} \mathbb {P}_{\ne 0}\left(a \mathbb {P}_{\ge k} f\right)\right\Vert _{L^{p}\left(\mathbb {T}^{3}\right)} \lesssim k^{-1}\left\Vert \nabla ^{2} a\right\Vert _{L^{\infty }\left(\mathbb {T}^{3}\right)}\Vert f\Vert _{L^{p}\left(\mathbb {T}^{3}\right)},\) 
